Existence of densities for jumping stochastic differential equations

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:116

Article

Fournier, N ; Giet, JS

关键词: stochastic differential equations;    jump processes;    absolute continuity;   

DOI  :  10.1016/j.spa.2005.11.002

来源: Elsevier

【 摘 要 】

We consider a jumping Markov process {X-t(x)}(t >= 0). We study the absolute continuity of the law of X-t(x) for t > 0. We first consider, as Bichteler and Jacod [K. Bichteler, J. Jacod, Calcul de Malliavin pour les diffusions avec sauts, existence d'une densite dans le cas unidimensionel, in: Seminaire de Probabilites XVII, in: L.N.M., vol. 986, Springer, 1983, pp. 132-157] did, the case where the rate of jumping is constant. We state some results in the spirit of those of [K. Bichteler, J. Jacod, Calcul de Malliavin pour les diffusions avec sauts, existence d'une densite dans le cas unidimensionel, in: Seminaire de Probabilites XVII. in: L.N.M., vol. 986, Springer, 1983, pp. 132-157], with rather weaker assumptions and simpler proofs, not relying oil the use of stochastic calculus of variations. We next extend our method to the case where the rate of jumping depends on the spatial variable, and this last result seems to be new. (C) 2005 Elsevier B.V. All rights reserved.

【 授权许可】

Free